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Repetitive transients are usually generated in the monitoring data when a fault occurs on the machinery. As a result, many methods such as kurtogram and optimized Morlet wavelet and kurtosis method are proposed to extract the repetitive transients for fault diagnosis. However, one shortcoming of these methods is that they are constructed based on the index of kurtosis and are sensitive to the impulsive noise, leading to failure in accurately diagnosing the fault of the machinery operating under harsh environment. To address this issue, an optimized SES entropy wavelet method is proposed. In the proposed method, the optimized parameters including bandwidth and central frequency of Morlet wavelets are selected. Then, based on the wavelet coefficients decomposed using the optimized Morlet wavelet, the SES entropy is calculated to select the scales of wavelet coefficients. Finally, the repetitive transients are reconstructed based on the denoising wavelet coefficients of the selected scales. One simulation case and vibration data collected from the experimental setup are used to verify the effectiveness of the proposed method. The simulated and experimental analyses showed that the signal-to-noise ratio (SNR) of the proposed method has the largest value. Specifically, the SNR in the experimental analysis of the proposed method is 0.6, while that of the other three methods is 0.043, 0.0065, and 0.0045, respectively. Therefore, the result shows that the proposed method is superior to the traditional methods for repetitive transient extraction from the vibration data suffered from impulsive noise.

This article addresses the problem of distributed joint estimation for a class of discrete‐time time‐varying systems subject to random nonlinearities and unknown inputs over sensor networks. For the purpose of energy‐saving, the dynamic event‐triggering mechanism is adopted to govern the signal transmission between the sensor and the local estimator. First, some constraint conditions are introduced to decouple the unknown input to eliminate their impact. Then, by means of mathematical induction, an upper bound of the filtering error covariance is individually obtained for the state and the unknown input by solving coupled Riccati‐like difference equations. Subsequently, the matrix simplification method is adopted to tackle the sparsity problem caused by sensor networks. In addition, the required distributed estimator gains are acquired by minimizing the obtained upper bounds of filtering error covariances. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed joint estimator design scheme.

The typical power transformer diagnosis approach is imprecise and unstable. A support vector machine classification algorithm is proposed, by designing an algorithm program that can improve the accuracy and speed of energy transformer diagnosis, the vibration signals of the surface twisting in different states are extracted by wavelet packet energy spectrum signal processing method, it is verified that the curve similarity between the vibration simulation model and the measured data is greater than 0.98, proving the simulation model’s validity. The calculation technique of online short circuit inductance is developed from the equivalent transformer model, and the variation error of simulation results is less than 0.05% when compared to the real transformer characteristics. The suggested state diagnostic technique successfully compensates for the drawbacks of the reactance method, which is incapable of detecting and judging the slightly loose or faulty winding. The method’s accuracy and superiority, as well as the practicability of the state diagnosis system, are demonstrated.